arXiv subjects

N. G. Grulha Jr.

Publications and source records attributed to N. G. Grulha Jr..

4 recordsLinked to original sources

arXiv2026

Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings

We make a detailed investigation of the generic properties that polynomial mappings possess. An important starting point is the work by Farnik, Jelonek and Ruas in 2019, where they prove some of those properties in the context of homogeneous polynomial mappings of $\mathbb{C}^3$ to $\mathbb{C}^3$, and conclude the genericity of $\mathcal{A}$-finite determinacy by applying the geometric criterion. Using their strategy, we further extend and generalize some of their key findings to dimensions greater than or equal to $2$, though some of those properties can only be extended up to dimension $4$.

math.AG↗

arXiv2026

Poincaré-Hopf Theorem for Isolated Determinantal Singularities

Let $X$ be a projective algebraic $d$-variety endowed with isolated determinantal singularities, and let $ω$ be a $1$-form on $X$ exhibiting a finite number of singularities (in the stratified sense). Under some technical conditions, we use two generalizations of Poincaré-Hopf index with the goal of proving a Poincaré-Hopf Type Theorem for $X$.

math.GT↗

arXiv2026

Poincaré-Hopf Theorem for Isolated Determinantal Singularities

Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated determinantal singularities and $ω$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense). Under some technical conditions on $r$ we use two generalization of Poincaré-Hopf index with the goal of proving a Poincaré-Hopf Type Theorem for $X$.

math.GT↗

arXiv2020

Results on Milnor Fibrations for mixed polynomials with non-isolated singularities

In this article we investigate mixed polynomials and present conditions that can be applied on a specific class of polynomials in order to prove the existence of the Milnor Fibration, Milnor-Lê Fibration and the equivalence between them. We prove for this class the of functions that the Milnor-Lê fiber on a regular value is homeomorphic to the Milnor-Lê fiber on a critical value. We develop a criterion to verify the transversality property and apply it to a special case of the class of mixed polynomial.

math.AG↗